Your use of grep was wrong. It's for testing lists - you just wanted a single match there. The redo isn't wrong, but can catch someone off guard. Overall the thing looks much like C. More idiomatically, it looks like this:

use Term::ReadKey;

sub Request {
  my ($prompt, $letters, $linefeed) = @_;

  return unless $prompt;
  $letters ||= "Ny";
  $linefeed ||= 1;

  my ($answer, $is_correct);
  do {
      print "$prompt? [$letters] ";

      ReadMode 'cbreak';
      $answer = uc ReadKey 0;
      ReadMode 'normal';

      $is_correct = (index uc $letters, $answer >= 0);
      print "\nplease answer [$letters]\n" unless $is_correct;
  } until $is_correct;

  print "\n" if $linefeed;

  return $answer;
}
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Note the use of uc to force things to uppercase so we needn't juggle with case-insensitivity in comparisons. You can then use it as in if(Request(...) eq 'Y') { ... }.

Update: Oops. Now complies with strict.

Makeshifts last the longest.